This invention relates to filters and, more particularly, to filter banks for audio applications.
In many areas of audio processing, it is desirable to analyze an audio signal in approximately the same time-frequency form as the human ear (i.e., with bandwidths on the order of one Bark) and with a time resolution that is commensurate with the bandwidth of the filter. In addition, it is desirable to process the signals in each of the bands and then reconstruct them in a manner such that when the bands are unmodified, the filter bank has a nearly perfect reconstruction characteristic. Because the signals might be modified, and different bands might be routed to different devices, not only must the filters provide approximately exact reconstruction, they must also prevent aliasing due to the unequal processing, or modification, of adjacent frequency bands. Hence, an oversampled filter bank is required where aliasing introduced due to unequal processing of bands is below the level of human hearing.
One application for this kind of filter bank is found for the problem of separating parts of an individual audio signal into its directs and indirect parts for the purpose of rerouting, in real time, the direct and indirect signals to drivers that reproduce them appropriately. In such an application, a filter bank that approximates the critical bandwidths is essential to identifying the part of a signal with direct cues, and the ability of the reconstruction filter bank to prevent substantial aliasing when adjacent bands are added incoherently (as opposed to coherently) is also an absolute requirement. Hence the need for an oversampled critical band filter bank. In applications that require nonuniform division of signal spectrum, iterative cascaded of uniform filter banks are often used. Iterated filter banks, however, impose considerable structure on the equivalent filters, which results in inferior time-frequency localization compared to direct designs. A study of critically sampled nonuniform filter banks has been reported by J. Princen in “The Design of Nonuniform Filter Banks,” IEEE Transactions on Signal Processing, Vol. 43, No. 11, pp. 2550–2560, November 1995. Nonuniform filter banks studied by Princen are obtained by joining pseudo QMF filter bank sections that are nearly perfect reconstruction filter banks based on cosine modulation and the principle of adjacent channel aliasing cancellation. R. Bernardini et al published “Arbitrary Tilings of the Time-Frequency Plane using Local Bases,” IEEE Transactions on Signal Processing, Vol. 47, No. 8, pp. 2293–2304, August 1999, wherein they describe a cosine-modulation-based structure that allows for time-adaptive nonuniform tiling of the time-frequency plane. Despite their many fine features that are relevant to coding purposes, however, these approaches do not have good aliasing attenuation properties in each of the subbands independently. This makes them unsuitable for tasks where processing effects need to be contained within the bands directly affected. Perfect, or nearly perfect, reconstruction properties of these filter banks in the presence of upsampling are also not clear. The pseudo QMF bank, for instance, loses its aliasing cancellation property if the subband components are not critically downsampled.
Oversampled uniform filter banks based on cosine modulation were studied by Bolceskei et al, and reported in “Oversampled Cosine Modulated Filter Banks with Perfect Reconstruction, IEEE Transaction on Circuits and Systems II, Vol. 45, No. 8, pp. 1057–1071, August 1998, but the cosine modulation places stringent aliasing attenuation requirements.